PRIMARY 4 MATHEMATICS LEARNING GUIDE · BATCH 10 · GUIDE 38
A practice paper is most useful when it produces a map of what to repair next. A total score can show how many marks were lost. It cannot, by itself, tell us whether the loss came from place value, fraction meaning, decimal alignment, graph scale, multi-step sequencing or an avoidable execution error.
This page contains an original eduKate Primary 4 Mathematics paper written for retrieval, mixed-topic selection and post-paper diagnosis. It does not reproduce past-year examination questions and is not presented as an official school paper. Schools differ in paper structure, mark allocation and timing; follow the actual school’s current instructions for formal assessment preparation.
The content stays within the Primary 4 learning estate and selected problem-solving heuristics already owned by the hub. The official curriculum reference is the MOE Primary Mathematics Syllabus, updated October 2025.
Series route: Primary 4 Mathematics Learning Hub. For a focused heuristic owner, use Assumption Method.
Navigate: instructions · Section A · Section B · solutions A · solutions B · diagnosis · repair routing.
1. How to use this paper
Attempt the paper without the worked solutions open. Show ordinary working for questions where the route is not immediate.
Mark each question after the attempt, then classify each error before doing another paper.
Suggested classifications:
- read the question incorrectly;
- relationship or concept not understood;
- representation chosen poorly;
- correct method, inaccurate calculation;
- multi-step order lost;
- final interpretation or unit wrong;
- did not check a suspicious answer.
This paper can be done as one full mixed review or split into smaller sections. It is not necessary to imitate an examination time limit during the first diagnostic attempt.
2. Before starting: predict the likely weak areas
Write three topics you expect to find easy and three that may need checking. After the paper, compare prediction with evidence.
This calibration step is useful because confident misconceptions and unnecessary uncertainty need different responses.
Do not change answers merely because a topic “felt weak”. Use mathematical checks.
3. Section A · Core arithmetic and representation
- What is the value of the digit 8 in 48,306?
- Arrange 39,508; 39,850; 38,950; 40,005 from smallest to largest.
- Round 67,451 to the nearest hundred.
- Estimate 398 × 21 using convenient nearby numbers.
- Calculate 3,406 + 18,795.
- Calculate 20,000 − 8,746.
- Calculate 2,408 × 6.
- Calculate 324 × 27.
- Calculate 2,436 ÷ 7.
- Calculate 1,248 ÷ 6.
- List all factors of 24.
- Find the common factors of 18 and 30.
- Find the first positive common multiple of 6 and 8.
- Convert 13/4 to a mixed number.
- Convert 2 3/5 to an improper fraction.
- Calculate 3/4 + 1/6.
- Calculate 5/6 − 1/4.
- Find 3/5 of 45.
- Order 3.08, 3.8, 3.18 and 3.081 from smallest to largest.
- Round 4.449 directly to one decimal place.
4. Section A · Geometry, measurement and data
- A rectangle has area 96 cm² and width 8 cm. Find its length.
- Find the perimeter of the rectangle in Question 21.
- A square has perimeter 36 cm. Find its side and area.
- A 14 cm by 10 cm rectangle has a 5 cm by 4 cm corner removed. Find the remaining area.
- For the same corner-cut figure, find the perimeter by tracing the exterior boundary.
- An acute angle is measured as 128°. Explain what should be checked before accepting the answer.
- A graph has labelled values 20 and 40 separated by four equal gaps. What does one gap represent?
- A pie chart represents 80 pupils. One quarter belongs to Group A. Find Group A.
- 3.6 L and 850 mL are combined. Give the total in litres.
- 5 kg 200 g − 2 kg 650 g = ?
5. Section B · Mixed reasoning and word problems
- A has four times as many beads as B. Together they have 210 beads. Find both amounts.
- A has six times as many tokens as B and has 140 more tokens than B. Find both.
- After receiving 149 stickers, Hana has 580. How many did she have before receiving them?
- A shop starts with 416 bottles, receives 89 and finishes with 367 after selling some. How many bottles were sold?
- A box contains 72 counters. One third are used. Then one quarter of the remainder are used. How many remain?
- 197 people need vehicles that hold 8 people each. What is the minimum number of vehicles required?
- Two amounts total 174 and differ by 38. Find both amounts.
- Three eighths of a collection are 27 counters. Find the whole collection.
- Nine boxes contain 24 markers each. Fifty-seven markers are used. The rest are shared equally among three groups. How many markers does each group receive?
- Twenty tickets cost either $7 or $4. The total collection is $101. Find how many of each ticket were sold.
- A tank contains 2.8 L. Another 650 mL is added, then 900 mL is used. How much remains?
- A programme starts at 2:40 p.m. and lasts 1 h 35 min. When does it finish?
- A number is tripled and then 14 is added. The final result is 110. Find the starting number.
- Two equal boxes contain 48 counters altogether. How many counters are in each?
- Two boxes contain 48 counters altogether, but no equality or other relation is given. Can both amounts be found uniquely?
6. Section B · Communication and transfer
- Explain why 1.7 is greater than 1.65 using place value.
- Repair the false chain 48 + 27 = 75 × 2 = 150 without changing the intended two actions.
- Give a counterexample to “rectangles with equal area always have equal perimeter”.
- Translate “A has three times B; together they have 168” into equal units and solve.
- Create a smaller version of a difficult problem that preserves the relationship “one third of the original, then one quarter of the remainder”.
7. Optional extension · Search and pattern reasoning
- Use digits 0, 2 and 5 once each to list all ordinary three-digit numbers.
- Find all positive whole-number rectangle side pairs with area 36, counting rotations once.
- State the rule and next two terms: 4,250; 4,350; 4,450; 4,550.
- Find a counterexample to “every number ending in 2 is a multiple of 4”.
- An input-output table gives 1→5, 2→8, 3→11, 4→14. Predict the output for 10 and describe a rule.
8. Worked solutions · Section A questions 1–10
1. The 8 is in the thousands place. Value = 8,000.
2. 38,950; 39,508; 39,850; 40,005. Compare ten-thousands first, then thousands, hundreds and remaining places.
3. Neighbouring hundreds are 67,400 and 67,500. Midpoint = 67,450. Since 67,451 is above the midpoint, answer = 67,500.
4. 398≈400 and21≈20, so estimate ≈ 8,000.
5. 3,406 + 18,795 = 22,201.
6. 20,000 − 8,746 = 11,254.
7. 2,408×6 = 14,448.
8. 324×20=6,480; 324×7=2,268; total=8,748.
9. 2,436÷7 = 348. Check 348×7=2,436.
10. 1,248÷6 = 208. The zero records zero tens in the quotient.
9. Worked solutions · Section A questions 11–20
11. Factors: 1,2,3,4,6,8,12,24.
12. Common factors of18 and30: 1,2,3,6.
13. First positive common multiple of6 and8 = 24.
14. 13/4 = 3 1/4.
15. 2 3/5 = (2×5+3)/5 = 13/5.
16. 3/4=9/12 and1/6=2/12, so answer=11/12.
17. 5/6=10/12 and1/4=3/12, so answer=7/12.
18. 45÷5=9;9×3=27.
19. 3.08, 3.081, 3.18, 3.8. Compare 3.080,3.081,3.180,3.800.
20. Direct rounding to one decimal place gives 4.4 because the hundredths digit is4.
10. Worked solutions · Section A questions 21–30
21. Length=96÷8=12 cm.
22. Perimeter=12+8+12+8=40 cm.
23. Side=36÷4=9 cm; area=9×9=81 cm².
24. Full area=140 cm²; cutout=20 cm²; remaining=120 cm².
25. Exterior lengths14+6+5+4+9+10=48 cm.
26. An acute angle must be less than90°. Check the protractor scale and starting zero before accepting128°.
27. Difference=20 across4 gaps; one gap=5.
28. 80÷4=20 pupils.
29. 3.6 L=3,600 mL; +850=4,450 mL=4.45 L.
30. Regroup5 kg200 g as4 kg1,200 g; subtract2 kg650 g to get 2 kg550 g.
11. Worked solutions · Section B questions 31–40
31. B=1 unit,A=4 units,total=5 units. One unit=210÷5=42. B=42,A=168.
32. Difference=5 units=140. One=28. B=28,A=168.
33. Start=580−149=431 stickers.
34. Before sales=416+89=505. Sales=505−367=138 bottles.
35. One third of72=24; remain48. One quarter of48=12; remain=36.
36. 197÷8=24 remainder5. Twenty-four vehicles hold192; one more is needed. 25 vehicles.
37. Remove difference:174−38=136. Half=68. Larger=106. 68 and106.
38. Three units=27, one=9, eight=72.
39. 9×24=216;216−57=159;159÷3=53 markers per group.
40. Assume all $4:80. Shortage21. Difference3. Seven adult tickets. 7 at $7 and13 at $4.
12. Worked solutions · Section B questions 41–50
41. 2.8 L=2,800 mL. +650−900=2,550 mL=2.55 L.
42. 2:40 p.m.+1 h=3:40; +35 min=4:15 p.m.
43. Undo +14:110−14=96. Undo ×3:96÷3=32.
44. Equal boxes:48÷2=24 each.
45. No unique answer. Examples20+28 and17+31 both satisfy the total.
46. 1.7=1.70. Seven tenths exceeds six tenths, so 1.7>1.65.
47. Write 48+27=75, then75×2=150. Do not join unequal expressions with an equals sign.
48. 6×4 and8×3 rectangles both area24; perimeters20 and22. This disproves the universal claim.
49. Four total units=168; one=42. B=42,A=126.
50. One valid simpler case: use1/3 of24→8 used,16 remain; use1/4 of16→4 used; final12. The changing-whole relationship is preserved.
13. Optional extension solutions 51–55
51. 205,250,502,520. Leading zero is not allowed for ordinary three-digit numbers.
52. 1×36,2×18,3×12,4×9,6×6.
53. Add100. Next=4,650 and4,750.
54. 42 ends in2 but is not divisible by4.
55. Output rises by3 per input step; rule can be described as3×input+2. For10, output=32.
14. Turn the marked paper into an error map
Do not begin the next paper immediately.
For every wrong answer, identify the first divergence.
| Visible mistake | Possible first weak link |
|---|---|
| 1,248÷6 becomes28 | Placeholder zero/place value in division |
| 3/4+1/6 becomes4/10 | Unlike fraction units not equalised |
| 3.8 placed below3.18 | Decimal place value |
| 197÷8 reported as24 vehicles | Remainder interpretation |
| Composite perimeter uses area decomposition lines | Boundary versus region |
| Ticket problem divides shortage by $7 | Assumption replacement difference misunderstood |
Repair the first dependency, not every symptom that followed it.
15. Separate knowledge gaps from execution errors
If the learner can explain why 3/4 and1/6 need common units but makes one arithmetic slip converting the numerator, the concept and execution layers should be recorded separately.
If the learner has no explanation for why denominators cannot simply be added, concept repair comes first.
Likewise, a correct bar model followed by inaccurate division does not require reteaching the model.
This distinction makes revision more efficient.
16. Identify questions left blank for different reasons
A blank can mean the concept was unavailable, the learner did not recognise the problem type, the question appeared time-consuming or the learner ran out of time.
Ask what happened before assigning a diagnosis.
For a timed practice later, record the last question attempted and the questions deliberately skipped.
Blank does not automatically mean “does not know”.
17. Use an independent check on suspicious correct answers
Correct answers reached through invalid reasoning can be unstable.
If a learner guesses 72 for the three-eighths question, ask them to show the unit structure.
If a learner gives25 vehicles, ask why24 is insufficient.
If the explanation survives a changed case, confidence in the capability rises.
A practice paper measures reasoning only when working is inspected where necessary.
18. Repair routing by question family
| Question family | Owner guide |
|---|---|
| Whole numbers, operations | Whole Numbers, Factors, Multiples and Four Operations |
| Fractions/decimals | Fractions, Decimals and Number Relationships |
| Geometry | Area, Perimeter, Angles, Symmetry and Nets |
| Data | Tables, Line Graphs, Pie Charts and Scale Reading |
| Assumption heuristic | Assumption Method |
| Mixed representation/selection | Mixed Problem Laboratory |
19. Build a short repair set from the evidence
Choose three to five questions that target the same first weak link with controlled variations.
Example: if decimal comparison failed, use3.6 versus3.56,2.08 versus2.8, and4.70 versus4.7.
Then return to one mixed question after the repair.
Do not assign fifty unrelated questions because one concept failed.
The next paper should test whether the repaired relationship survives transfer.
20. When to introduce timing
Timing becomes useful after the learner can solve the content with reasonable reliability.
If a concept is unknown, a stopwatch mainly measures how quickly the learner becomes stuck.
Use an untimed diagnostic first when necessary. Then introduce a realistic paper or section time based on the school’s current format.
Track time lost to rereading, long calculations, checking and getting stuck separately when possible.
Speed should grow from recognition and efficient working, not skipped reasoning.
21. A practice-paper cycle
- Attempt.
- Mark.
- Classify each error.
- Identify the first weak links.
- Repair narrowly.
- Retest with changed questions.
- Return to another mixed paper later.
Repeated papers without the repair stages can reproduce the same error pattern.
The paper is a measurement instrument inside the learning loop, not the loop itself.
22. Parent and teacher communication
A useful note says: “Division meaning is secure, but placeholder zeros caused two errors,” or “Fraction procedures were correct until the reference whole changed.”
This is more actionable than “Scored 72%”.
Include whether a prompt, worked example or calculator was used if relevant to the learning record.
Do not represent an independently written eduKate practice paper as a school paper.
23. Handover to revision strategy
A practice paper tells us what happened under mixed retrieval. Revision strategy decides what to do with that evidence.
Continue to Revision Strategy: Topic Checklist, Weak-Link Repair and Assessment Readiness.
Final checkpoint: can the learner turn each lost mark into a specific mathematical explanation and route the next practice to the first unstable dependency rather than simply doing another full paper?
Source and editorial note
The content boundary is referenced to the MOE Primary Mathematics Syllabus, updated October 2025. Every question in this practice paper is independently written by eduKate Publishing.
Editorial control: Wintour House V1.0 · CivDJ · eduKate Publishing.
